{"product_id":"9781786300133-partial-differential-equations","title":"Integration","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003e\u003cp\u003eThis book presents a simple and novel theory of integration, both real and vectorial, particularly suitable for the study of PDEs. This theory allows for integration with values in a Neumann space E, i.e. in which all Cauchy sequences converge, encompassing Neumann and Fréchet spaces, as well as \"weak\" spaces and distribution spaces.\u003c\/p\u003e \u003cp\u003eWe integrate \"integrable measures\", which are equivalent to \"classes of integrable functions which are a.e. equals\" when E is a Fréchet space. More precisely, we associate the measure f with a class f, where f(u) is the integral of fu for any test function u. The classic space Lp(Ω;E) is the set of f, and ours is the set of f; these two spaces are isomorphic.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntegration\u003c\/i\u003e studies, in detail, for any Neumann space E, the properties of the integral and of Lp(Ω;E): regularization, image by a linear or multilinear application, change of variable, separation of multiple variables, compacts and duals. When E is a Fréchet space, we study the equivalence of the two definitions and the properties related to dominated convergence.\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":57396567867766,"sku":"9781786300133","price":159.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/stand_40302871.jpg?v=1773290281","url":"https:\/\/www.rarewaves.com\/products\/9781786300133-partial-differential-equations","provider":"Rarewaves.com","version":"1.0","type":"link"}